Centre for Advanced Study

at the Norwegian Academy of Science and Letters

Nonlinear Partial Differential Equations

Information

Former 2008/2009 Natural Sciences - Medicine - Mathematics

Abstract

The research program will focus on the mathematical discipline nonlinear partial differential equation. Differential equations have their origin in the quest to describe nature by mathematics, and these equations are perfect tools to describe physical phenomena that vary in space and time. In fact, all the fundamental laws of nature are given by differential equations (Newton’s law describes gravitation, Maxwell’s equations describe electromagnetism, Navier–Stokes’ equations describe fluid flow, etc). Thus they model a wide variety of phenomena, and have been extensively studied by mathematicians, physicists, engineers, and others. Differential equations constitute a core mathematical discipline, cf. the Abel Prize 2005. However, several key questions have not been answered, or only been partly answered. Central issues are: • Do the equations have a solution? It is still not known if the equations that describe the flow of air around an airplane have a solution. • Given that the equation has a solution, is it unique? For flow of oil in petroleum reservoirs the equations give several possible distinct values for the saturation at the same point in space. • Is the solution stable? Will a small change in one place in space have dramatic consequences in a completely different location (“the butterfly effect"). • If the equation has a unique and stable solution, how can one determine the solution? Given the measured weather data for today, how can one predict the weather for tomorrow? Variations of these questions for carefully selected nonlinear partial differential equations constitute the focus for the research program, in particular the interplay between theoretical results (mathematical properties of the solution) and numerical computations (how to compute the solution). Differential equations have been an intensive research area in mathematics in Norway the last two decades, and there are now strong research groups in Oslo, Trondheim, and Bergen. The research program will both benefit from the strong national activities and further strengthen it. Furthermore, applications to other areas of science will have impact there. The generic nature of mathematics means that the methods and techniques of this program can be applied to several seemingly distinct areas. We will focus on four applications, namely flow in porous media (e.g., flow of oil in a petroleum reservoir), mixtures of solids and fluids (e.g., sedimentation), gas dynamics (e.g., flow of gas around obstacles), water waves (e.g., breaking of waves).

Fellows

  • Amadori, Debora
    Dr. University of L'Aquila 2008/2009
  • Andreianov, Boris Andreianov
    Dr. University of Franche-Comté 2008/2009
  • Brenier, Yann
    - University of Nice 2008/2009
  • Bressan, Alberto
    Professor Pennsylvania State University 2008/2009
  • Carrillo de la Plata, Jose Antonio
    Professor Catalan Institution for Research and Advanced Studies (ICREA) 2008/2009
  • Chen, Gui-Qiang G.
    Professor University of Oxford 2008/2009
  • Coclite, Giuseppe Maria
    Assistant Professor University of Bari 2008/2009
  • Feireisl, Eduard
    Professor Institute of Mathematics of the Czech Academy of Sciences 2008/2009
  • Frid, Hermano
    Professor Instituto de Matemática Pura e Aplicada (IMPA) 2008/2009
  • Gesztesy, Fritz
    Professor University of Missouri 2008/2009
  • Hanche-Olsen, Harald
    Associate Professor Norwegian University of Science and Technology (NTNU) 2008/2009
  • Jakobsen, Espen Robstad
    Associate Professor Norwegian University of Science and Technology (NTNU) 2008/2009
  • Jenssen, Kristian
    Associate Professor Pennsylvania State University 2008/2009
  • Kalisch, Henrik
    Associate Professor University of Bergen (UiB) 2008/2009
  • Karper, Trygve Klovning
    Research Fellow Norwegian University of Science and Technology (NTNU) 2008/2009
  • Klainerman, Sergiu
    Professor Princeton University 2008/2009
  • Kwon, Young-Sam
    Dr. University of Maryland 2008/2009
  • LeFloch, Philippe Gerard
    Professor Pierre and Marie Curie University 2008/2009
  • Lindqvist, Lars Peter
    Professor Norwegian University of Science and Technology (NTNU) 2008/2009
  • Liu, Hailiang
    Professor Iowa State University 2008/2009
  • Panov, Evgeniy Yuz'evich
    Professor Novgorod State University 2008/2009
  • Raynaud, Xavier Marcel
    - University of Oslo (UiO) 2008/2009
  • Risebro, Nils Henrik
    Professor University of Oslo (UiO) 2008/2009
  • Rohde, Christian
    Professor University of Stuttgart 2008/2009
  • Sande, Hilde
    - Norwegian University of Science and Technology (NTNU) 2008/2009
  • Selberg, Sigmund
    Associate Professor Norwegian University of Science and Technology (NTNU) 2008/2009
  • Serre, Denis
    Professor ENS de Lyon 2008/2009
  • Shen, Wen
    Assistant Professor Pennsylvania State University 2008/2009
  • Tadmor, Eitan
    Professor University of Maryland 2008/2009
  • Teschl, Gerald
    Professor University of Vienna 2008/2009
  • Towers, John David
    Professor Mira Costa College 2008/2009
  • Trivisa, Konstantina
    Professor University of Maryland 2008/2009
  • Zhaoyang, Yin
    Professor Zhongshan University 2008/2009

Previous events

Group leader

  • Helge Holden

    Title Professor Institution Norwegian University of Science and Technology (NTNU) Year at CAS 2008/2009
  • Kenneth H. Karlsen

    Title Professor Institution University of Oslo (UiO) Year at CAS 2008/2009
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